Common Notation
We use these notations:
- A is a set of X positive integers, and Ad is its subset of integers divisible by d
- w(d) and Rd are functions of A and of d that estimate the number of elements of A that are divisible by d, according to the formula
- Thus w(d) / d represents an approximate density of members divisible by d, and Rd represents an error or remainder term.
- P is a set of primes, and P(z) is its the product of those primes ≤ z
- S(A, P, z) is the number of elements of A not divisible by any prime in P that is ≤ z
- κ is a constant, called the sifting density, that appears in the assumptions below. It is a weighted average of the number of residue classes sieved out by each prime.
Read more about this topic: Fundamental Lemma Of Sieve Theory
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